A uniform rod of mass M = 250.0 g and length L = 50.0 cm stands vertically on a

Question

A uniform rod of mass M = 250.0 g and length L = 50.0 cm stands vertically on a horizontal table. It is released from rest to fall.

a) Which of the following forces are acting on the rod?

1-normal force ,2-force of friction ,3-tension force , 4-gravitational force , 5-spring force

b) Calculate the angular speed of the rod as it makes an angle (theta) = 45? with respect to the vertical.

c) Calculate the vertical acceleration of the moving end of the rod as it makes an angle (theta) = 45? with respect to the vertical (take upward as positive and downward as negative).

d) Calculate the normal force exerted by the table on the rod as it makes an angle (theta) = 45? with respect to the vertical.

e) If the rod falls onto the table without slipping, find the linear acceleration of the end point of the rod when it hits the table.

Explanation / Answer

a)1,2,4
b)Friction exist but is not doing any work, hence energy can be conserved.
Therefore, mgh/2 = mg(h/2)/2 +1/2 mv^2

on solving, v = 1.21 m/s

Hence, = 4.84rad/s

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